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1)3.8.2-5.8
=8(6-5)=8
2)4.25-32:8
=4(25-1)=4.24=96
3)3.25-16:4
=75-4=71
4)4.25-3.8
=4(25-6)
=4.19=76
\(\left(2x-2\right).2024=0\)
\(\left(2x-2\right)=0\div2024\)
\(2x-2=0\)
\(2x=0+2\)
\(2x=2\)
\(x=1\)
\(15\div\left(6-x\right)=5\)
\(\left(6-x\right)=15\div5\)
\(6-x=3\)
\(x=6-3\)
\(x=3\)
\(\left[\left(10-x\right).2+5\right]\div3-2=3\)
\(\left[\left(10-x\right).2+5\right]\div3=3+2\)
\(\left[\left(10-x\right).2+5\right]\div3=5\)
\(\left(10-x\right).2+5=5.3\)
\(\left(10-x\right).2+5=15\)
\(\left(10-x\right).2=15-5\)
\(\left(10-x\right).2=10\)
\(\left(10-x\right)=10\div2\)
\(10-x=5\)
\(x=10-5\)
\(x=5\)
\(134\div\left(x-3\right)=35+160\div5\)
\(134\div\left(x-3\right)=35+32\)
\(134\div\left(x-3\right)=67\)
\(\left(x-3\right)=134\div67\)
\(x-3=2\)
\(x=2+3\)
\(x=5\)
e) \(5^{x+1}+5^x=150\)
\(\Leftrightarrow5^x.5+5^x=150\)
\(\Leftrightarrow6.5^x=150\)
\(\Leftrightarrow5^x=25=5^2\)
\(\Leftrightarrow x=2\)
i) \(2345-1000\div\left[19-2\left(21-18\right)^2\right]\)
\(=\)\(2345-1000\div\left[19-2.3^2\right]\)
\(=\)\(2345-1000\div\left[19-2.9\right]\)
\(=\)\(2345-1000\div\left[19-18\right]\)
\(=\)\(2345-1000\div1\)
\(=\)\(2345-1000\)
\(=\)\(1345\)
j) \(128-\left[68+8\left(37-35\right)^2\right]\div4\)
\(=\)\(128-\left[68+8.2^2\right]\div4\)
\(=\)\(128-\left[68+8.4\right]\div4\)
\(=\)\(128-\left[68+32\right]\div4\)
\(=\)\(128-100\div4\)
\(=\)\(128-25\)
\(=\)\(3\)
k) \(568-\left\{5\left[143-\left(4-1\right)^2\right]+10\right\}\div10\)
\(=\)\(568-\left\{5\left[143-3^2\right]+10\right\}\div10\)
\(=\)\(568-\left\{5\left[143-9\right]+10\right\}\div10\)
\(=\)\(568-\left\{5.134+10\right\}\div10\)
\(=\)\(568-\left\{670+10\right\}\div10\)
\(=\)\(568-680\div10\)
\(=\)\(568-68\)
\(=\)\(500\)
a) \(107-\left\{38+\left[7.3^2-24\div6+\left(9-7\right)^3\right]\right\}\div15\)
\(=\)\(107-\left\{38+\left[7.3^2-24\div6+2^3\right]\right\}\div15\)
\(=\)\(107-\left\{38+\left[7.9-4+8\right]\right\}\div15\)
\(=\)\(107-\left\{38+\left[63-4+8\right]\right\}\div15\)
\(=\)\(107-\left\{38+67\right\}\div15\)
\(=\)\(107-105\div15\)
\(=\)\(107-7\)
\(=\)\(7\)
b) \(307-\left[\left(180-160\right)\div2^2+9\right]\div2\)
\(=\)\(307-\left[20\div4+9\right]\div2\)
\(=\)\(307-\left[5+9\right]\div2\)
\(=\)\(307-14\div2\)
\(=\)\(307-7\)
\(=\)\(300\)
c) \(205-\left[1200-\left(4^2-2.3\right)^3\right]\div40\)
\(=\)\(205-\left[1200-\left(16-6\right)^3\right]\div40\)
\(=\)\(205-\left[1200-10^3\right]\div40\)
\(=\)\(205-\left[1200-1000\right]\div40\)
\(=\)\(205-200\div40\)
\(=\)\(205-5\)
\(=\)\(200\)